Reflection coefficients of P-SV waves in weak anisotropic media

We introduce the Thomsen anisotropic parameters into the approximate linear reflection coefficient equation for P-SV wave in weakly anisotropic HTI media. From this we get a new, more effective, and practical reflection coefficient equation. We performed forward modeling to AVO attributes, obtaining excellent results. The combined AVO attribute analysis of PP and PS reflection data can greatly reduce ambiguity, obtain better petrophysical parameters, and improve parameter accuracy.

Wave Reflection by Rectangular Breakwaters for Coastal Protection

In this study,we focus on the numerical modelling of the interaction between waves and submerged structures in the presence of a uniform flow current.Both the same and opposite senses of wave propagation are considered.The main objective is an understanding of the effect of the current and various geometrical parameters on the reflection coefficient.The wave used in the study is based on potential theory,and the submerged structures consist of two rectangular breakwaters positioned at a fixed distance from each other and attached to the bottom of a wave flume.The numerical modeling approach employed in this work relies on the Boundary Element Method(BEM).The results are compared with experimental data to validate the approach.The findings of the study demonstrate that the double rectangular breakwater configuration exhibits superior wave attenuation abilities if compared to a single rectangular breakwater,particularly at low wavenumbers.Furthermore,the study reveals that wave mitigation is more pronounced when the current and wave propagation are coplanar,whereas it is less effective in the case of opposing current.

Improving seismic interpretation: a high-contrast approximation to the reflection coefficient of a plane longitudinal wave

Linearized approximations of reflection and transmission coefficients set a foundation for amplitude versus offset（AVO） analysis and inversion in exploration geophysics.However,the weak properties contrast hypothesis of those linearized approximate equations leads to big errors when the two media across the interface vary dramatically.To extend the application of AVO analysis and inversion to high contrast between the properties of the two layers,we derive a novel nonlinearized high-contrast approximation of the PP-wave reflection coefficient,which establishes the direct relationship between PPwave reflection coefficient and P-wave velocities,S-wave velocities and densities across the interface.（A PP wave is a reflected compressional wave from an incident compressional wave（P-wave）.） This novel approximation is derived from the exact reflection coefficient equation with Taylor expansion for the incident angle.Model tests demonstrate that,compared with the reflection coefficients of the linearized approximations,the reflection coefficients of the novel nonlinearized approximate equation agree with those of the exact PP equation better for a high contrast interface with a moderate incident angle.Furthermore,we introduce a nonlinear direct inversion method utilizing the novel reflection coefficient equation as forward solver,to implement the direct inversion for the six parameters including P-wave velocities,S-wave velocities,and densities in the upper and lower layers across the interface.This nonlinear inversion algorithm is able to estimate the inverse of the nonlinear function in terms of model parameters directly rather than in a conventional optimization way.Three examples verified the feasibility and suitability of this novel approximation for a high contrast interface,and we still could estimate the six parameters across the interface reasonably when the parameters in both media across the interface vary about 50%.

Experimental study of reflection coefficient and wave forces acting on perforated caisson

The reflection coefficient and the total horizontal forces of regular waves acting on theperforated caisson are experimentally investigated. The empirical relationship between reflection coefficient and the ratio of the total horizontal forces acting on the perforated caisson to those on solid vertical walls with the relative chamber width, relative water depth and porosity of perforated wall, etc. are given. Moreover, the results of the ratio of the total horizontal forces are also compared with formulas given by Chinese Harbour Design Criteria and Takahashi, which may be useful for the practical engineering application.

Ultrasonic characterization of modified Cr_2O_3 coatings by reflection coefficient spectroscopy

Pores,microcracks and density of plasma sprayed Cr2O3 coatings before and after high-intensity pulsed ion beam(HIPIB) irradiation were investigated using the ultrasonic reflection coefficient spectroscopy(URCS).The URCS was analyzed based on an acoustic transmission model for the multi-layered structure.The longitudinal velocity in the coatings was calculated from the experimental URCS,and the attenuation coefficient expression was deduced by comparing the experimental and numerical fitting amplitude spectral lines.The longitudinal velocity of as-sprayed Cr2O3 coating is 2 002 m/s,and increases to 2 099 and 2 148 m/s after being irradiated by HIPIB with 1 and 5 shots.Correspondingly,the factor A changes from 0.046 to 0.026 and 0.020 and n from 1.702 to 1.658 and 1.649 in the attenuation coefficient expression of α=Af n.It is observed that the surface morphology of Cr2O3 coatings changes from rough and porous to smooth and uniform with the increase of shot number,which accords with the ultrasonic analyses reasonably.The URCS seems to provide a convenient and nondestructive method to characterize surface modification of the plasma sprayed coatings.

Seismic reflection and transmission coefficients of a single layer sandwiched between two dissimilar poroelastic solids

The seismic reflection and transmission characteristics of a single layer sandwiched between two dissimilar poroelastic solids saturated with two immiscible viscous fluids are investigated. The sandwiched layer is modeled as a porous solid with finite thickness. The propagation of waves is represented with potential functions. The displacements of particles in different phases of the aggregate are defined in terms of these potential functions. Due to the presence of viscosity in pore fluids, the reflected and transmitted waves are inhomogeneous in nature, i.e., with different directions of propagation and attenuation. The closed-form analytical expressions for reflection and transmission coefficients are derived theoretically for appropriate boundary conditions. These expressions are calculated as a non-singular system of linear algebraic equations and depend on the various parameters involved in this non-singular system. Hence,numerical examples are studied to determine the effects of various properties of the sandwich layer on reflection and transmission coefficients. The essential features of layer thickness, incident direction, wave frequency, liquidsaturation and capillary pressure of the porous layer on reflection and transmission coefficients are depicted graphically and discussed. The analysis shows that reflection and transmission coefficients are strongly associated with incident direction and various properties of the porous layer.

Forward Modeling of the Relationship Between Reflection Coefficient and Incident Angle of the P Wave in a Coal Seam

Although the Zoeppritz equation is suitable for a single interface in a thick deposit, it has some limitations for composite reflection waves from both the floor and the roof of coal seams. Based on the ray model, the relationship of the overall reflection coefficient of composite reflection P waves, from coal seam versus incidence angle (AVO), is dis- cussed. The result shows that: 1) the overall reflection coefficient of composite reflection waves from coal seams is a negative value and is determined mainly by the lithology of roof and floor, which is different from the reflection coeffi- cient of a single interface; 2) if the incidence angle ranges from 0° to 6°, the reflection coefficient of composite waves of a coal seam does not change with the incidence angle and 3) if the incidence angle ranges from 6–60° , the reflection coefficient increases monotonically.

Calculation of Wave Reflection Coefficient for Perforated-Pipe Breakwater

The hollow-pipe perforated breakwater is of low reflection. In this paper the functions of reflection coefficients of both regular and random waves are theoretically derived, based on the concept of linear superimposition of reflected and incident waves and with the total flow rate continuity of integral form instead of the non-continuity of the boundary condition, and based on the concept of linear wave spectrum theory. Comparisons between theoretical results presented here and measurements of model tests show reasonable agreement.

A NOVEL METHOD FOR MEASURING COMPLEX REFLECTION COEFFICIENT USING A FOUR-PORT REFLECTOMETER

A novel method for precise measurement of complex reflection coeffcient using a four-port reflectometer is presented. First, three new complex system constants are introduced,which depend only on the scattering parameters of the four-port reflectometer. Therefore, the stability of the reflectometer is greatly improved. Then, these complex system constants are used to determine the complex reflection coeffcient F of the device under test by calibrating the reflectometer. Finally, a four-port reflectometer comprising a magic tee and a power detector is constructed and excellent experimental results are obtained.

Wave Reflection Coefficient Spectrum

The wave reflection coefficient frequency spectrum and directional spectrum for concrete face slope breakwaters and rubble mound breakwaters are investigated through physical model tests in the present study. The reflection coefficients of oblique irregular waves are analyzed by the Modified Two-Point Method (MTPM) proposed by the authors. The results show that the wave reflection coefficient decreases with increasing wave frequency and incident angle or decreasing structure slope. The reflection coefficient frequency spectrum and its variation with Iribarren number are given in this paper. The paper also suggests an empirical 3-dimensional reflection coefficient spectrum, i.e. reflection coefficient directional spectrum, which can be used to illustrate quantitatively the variation of reflection coefficient with the incident angle and the Iribarren number for oblique irregular waves.

Analysis of Directional Spectra and Reflection Coefficients in Incident and Reflected Wave Field

In this paper, the modified Bayesian method for the analysis of directional wave spectra and reflection coefficients is verified by numerical and physical simulation of waves. The results show that the method can basically separate the incident and reflected directional spectra. In addition, the effect of the type of wave gage arrays, the number of measured wave properties, and the distance between the wave gage array and the reflection line on the resolution of the method are investigated. Some suggestions are proposed for practical application.

Experimental Study on Reflection Coefficient of Curved Perforated Plate

A set of experiments is carried out in a towing tank to study the effects of the curvature of perforated plates on the wave reflection coefficient （Cr）. The curvature of a perforated plate can be changed by rotating a reference perforated plate about its origin point according to the parabolic equation y=-x2 A plunger-type wave maker is used to generate regular waves. The reflection coefficients are calculated using Goda and Suzuki’s （1976） method. The results are compared with those of vertical or sloped passive wave absorbers. The comparison shows that a perforated plate with a curved profile is highly efficient in terms of reducing the wave reflection coefficient. A correlation is established to estimate the reflection coefficient of curved perforated plates as a function of both flow and geometry characteristics.

A method of Robust low-angle target height and compound reflection coefficient joint estimation

It is always a challenging issue for radar systems to estimate the height of a low-angle target in the multipath propagation environment.The highly deterministic maximum likelihood estimator has a high accuracy,but the errors of the ground reflection coefficient and the reflecting surface height have serious influence on the method.In this paper,a robust es-timation method with less computation burden is proposed based on the compound reflection coefficient multipath model for low-angle targets.The compound reflection coefficient is es-timated from the received data of the array and then a one-di-mension generalized steering vector is constructed to estimate the target height.The algorithm is robust to the reflecting sur-face height error and the ground reflection coefficient error.Fi-nally,the experiment and simulation results demonstrate the validity of the proposed method.

Research on Thin Layer Structure Identification and Sedimentary Facies of Middle and Deep Layers Based on Reflection Coefficient Inversion—By Taking Dongying Formation of CFD Oilfield in Bohai Offshore as an Example

The sand layer B of Dongying Formation of CFD oilfield in Bohai offshore belongs to the middle deep layer of buried hill overlap deposit. Its reservoir distribution has the characteristics of large burial depth, thin thickness and rapidly lateral change. Because of low resolution of seismic data and overlying sand layer. It is difficult to identify and interpret the structure of sand layer accurately. The uncertainty of structure and reservoir restricts the fine development of B sand layer. In order to identify the top surface of reservoir effectively. The seismic data are processed by using the reflection coefficient inversion method. The results show that the inversion resolution of reflection coefficient is significantly higher than that of original data. The top surface of sand layer B and its overlying sand layer can be well identified and traced. Carrying out structural interpretation of B sand layer based on reflection coefficient inversion data and the microstructure and the formation tip extinction point are implemented. Based on the constraint of new interpretation level, the sedimentary facies plane distribution of B sand layer is described and make prediction of dominant reservoir development area in detail combining with sedimentary paleogeomorphology, along layer attribute section and limited drilling data. The research shows that the study area is mainly from the northwest material sources, the slope belt in the northwest is close to the lake shoreline with a gentle slope and shallow water depositional environment, which is located on the main transport and deposition channels. The shallow water gentle slope landform is suitable for forming large-area sand bar deposition, mainly composed of underwater distributary channel and debouch bars facies, which is the dominant reservoir development area. The research conclusion guides the deployment and implementation of the development well location effectively.

Algorithm and Design Methodology to Develop a PIFA with Optimized Reflection Coefficient for the ISM 868 MHz Band

This paper presents a methodological approach to design a printed Inverted F antenna for the ISM 868 MHz band. For this design, the ground plane dimensions were kept fixed and the meandered radiating arm was modified to obtain the best compromise integration/performances. This approach was then generalized to design meandered printed inverted F antennas.

Analysis of reflection coefficient for coated optical waveguide devices

From an ordinary condition,using a full three-dimensional model theory and an infinite perturbation expansion method,an exact solution of the reflection coefficient for the coated narrow stripe-geometry optical waveguide devices has been derived.All six components and the vector property of the electromagnetic field have been considered.The results are suitable for the symmetric and asymmetric waveguides.

Surface Reflection Coefficient of Impregnated RAM Honeycomb with Incident Normally Plan Wave to the Side Wall

The impregnated radar absorbing material(RAM) honeycomb is often used to fabricate parts of the war plane for reducing radar cross section. The incident wave vector may be divided into two components: one perpendicular to its hole and the other to its side wall. Until now, there has not been a program to calculate the input impedance or its equivalent electromagnetic parameters for the later case. In this paper, an approach for analyzing the reflection characteristics of the impregnated honeycomb when its side wall faces the incident plane wave is proposed. Experiments prove it an effective, accurate and fast solution to this subject.

P-P波和P-SV波联合AVO反演研究

目前转换波AVO(Amplitude Versus Offset)反演或纵波、转换波联合AVO反演是基于Aki等的反射系数近似公式,通常反演结果为上、下层速度比值和速度平均比值.本文在Shuey和郑晓东近似公式的基础上,运用最小平方算法,提出一种P-P波和P-SV波联合AVO反演下层介质纵、横波速度及泊松比的方案,并应用于双层含气砂岩模型上,误差在10%以内.此方案要求上、下层物性差别不大且入射角小于30°,但不需要速度比值为常数2的假设.

P-SV转换波反射系数与野外采集观测系统设计

本文用Zoeppritz方程对不同类型界面计算P波入射时P波与SV波的反射系数。通过分析，总结了P波与SV波位移反射系数随入射角的变化规律，用以指导P－SV转换波地震勘探的野外采集观测系统设计，并结合大庆某工区转换波勘探试验得出相应的结论。